 Rhombus ◦ A rhombus is a parallelogram with four congruent sides.

 Rectangle ◦ A rectangle is a parallelogram with four right angles.

 Square ◦ A square is a parallelogram with four congruent sides and four right angles.

RRhombus corollary ◦A◦A quadrilateral is a rhombus if and only if it has four congruent sides. RRectangle corollary ◦A◦A quadrilateral is a rectangle if and only if it has four right angles. SSquare corollary ◦A◦A quadrilateral is a square if and only if it is a rhombus and a rectangle.

 PQRS is a rhombus. What is the value of b? P Q R S 2b + 3 5b – 6 2b + 3 = 5b – 6 9 = 3b 3 = b

 In rectangle ABCD, if AB = 7f – 3 and CD = 4f + 9, then f = ___ A) 1 B) 2 C) 3 D) 4 E) 5 7f – 3 = 4f + 9 3f – 3 = 9 3f = 12 f = 4

 PQRS is a rhombus. What is the value of b? P Q R S 3b b – 6 3b + 12 = 5b – 6 18 = 2b 9 = b

 A parallelogram is a rhombus if and only if its diagonals are perpendicular.  A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. L

 A parallelogram is a rectangle if and only if its diagonals are congruent. A B CD

1. The diagonals are congruent 2. Both pairs of opposite sides are congruent 3. Both pairs of opposite sides are parallel 4. All angles are congruent 5. All sides are congruent 6. Diagonals bisect the angles A. Parallelogram B. Rectangle C. Rhombus D. Square B,D A,B,C,D B,D C,D C

Decide if the statement is sometimes, always, or never true. 1.A rhombus is equilateral. 2. The diagonals of a rectangle are _|_. 3. The opposite angles of a rhombus are supplementary. 4. A square is a rectangle. 5. The diagonals of a rectangle bisect each other. 6. The consecutive angles of a square are supplementary. Always Quadrilateral ABCD is Rhombus. 7. If m <BAE = 32 o, find m<ECD. 8. If m<EDC = 43 o, find m<CBA. 9. If m<EAB = 57 o, find m<ADC. 10. If m<BEC = (3x -15) o, solve for x. 11. If m<ADE = ((5x – 8) o and m<CBE = (3x +24) o, solve for x 12. If m<BAD = (4x + 14) o and m<ABC = (2x + 10) o, solve for x. A B E D C 32 o Sometimes Sometimes Always Always Always 86 o 66 o 35 o 16 26

Coordinate Proofs Using the Properties of Rhombuses, Rectangles and Squares Using the distance formula and slope, how can we determine the specific shape of a parallelogram? Rhombus – Rectangle – Square - Based on the following Coordinate values, determine if each parallelogram is a rhombus, a rectangle, or square. P (-2, 3)P(-4, 0) Q(-2, -4)Q(3, 7) R(2, -4)R(6, 4) S(2, 3)S(-1, -3) 1. Show all sides are equal distance 2. Show all diagonals are perpendicular. 1. Show diagonals are equal distance 2. Show opposite sides are perpendicular Show one of the above four ways. RECTANGLE